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S -classes infinitésimales d’un corps de nombres algébriques

Jean-François Jaulent (1984)

Annales de l'institut Fourier

Nous introduisons les notions de nombres et d’idéaux infinitésimaux attachés à un corps de nombres algébriques K relativement à un nombre premier donné ℓ , et nous interprétons le groupe de Galois 𝒜 ( K ) de la ℓ -extension abélienne ℓ -ramifiée maximale de K comme quotient du tensorisé Z ℓ ⊗ Z J ( K ) du groupe des idéaux étrangers à ℓ par le sous-module engendré par les idéaux principaux-infinitésimaux. Nous en déduisons diverses conséquences sur l’arithmétique des groupes 𝒜 ( K ) , en montrant en particulier qu’ils donnent...

Sekiguchi-Suwa theory revisited

Ariane Mézard, Matthieu Romagny, Dajano Tossici (2014)

Journal de Théorie des Nombres de Bordeaux

We present an account of the construction by S. Sekiguchi and N. Suwa of a cyclic isogeny of affine smooth group schemes unifying the Kummer and Artin-Schreier-Witt isogenies. We complete the construction over an arbitrary base ring. We extend the statements of some results in a form adapted to a further investigation of the models of the group schemes of roots of unity.

Some identities of degenerate special polynomials

Dae San Kim, Taekyun Kim (2015)

Open Mathematics

In this paper, by considering higher-order degenerate Bernoulli and Euler polynomials which were introduced by Carlitz, we investigate some properties of mixed-type of those polynomials. In particular, we give some identities of mixed-type degenerate special polynomials which are derived from the fermionic integrals on Zp and the bosonic integrals on Zp.

Some new directions in p -adic Hodge theory

Kiran S. Kedlaya (2009)

Journal de Théorie des Nombres de Bordeaux

We recall some basic constructions from p -adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of B -pairs, introduced recently by Berger, which provides a natural enlargement of the category of p -adic Galois representations. (This enlargement, in a different form, figures in recent work of Colmez, Bellaïche, and Chenevier on trianguline representations.) We also discuss results of Liu that indicate that the formalism of Galois cohomology, including Tate...

Some results on local fields

Akram Lbekkouri (2013)

Annales UMCS, Mathematica

Let K be a local field with finite residue field of characteristic p. This paper is devoted to the study of the maximal abelian extension of K of exponent p−1 and its maximal p-abelian extension, especially the description of their Galois groups in solvable case. Then some properties of local fields in general case are studied too.

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